We argue that by relying on complicated algebraic equations to induce linear dependencies in the latent structure, the SEM framework risks losing statistical rigor especially when modeling complex phenomena. Real data, most often than not, is noisy and characterized by complex nonlinear dependencies. We think that we have a better and more statistically rigorous alternative in the probabilistic generative perspective that approaches the modeling endeavor by first proposing a probabilistic model for all the observed variables and any latent variables that we wish to incorporate in the model. As part of the probabilistic model, we can also specify functional relations between the variables in order to capture any nonlinear dependencies in the data or to construct a rich latent space with complex structure. For example, a recent method, the Inverse Autoregressive Flow (IAF)[1]}, has been proposed in the generative modeling literature that enables us to create models with rich latent structure. The key idea behind the IAF is that any multivariate normal variable with diagonal covariance can be transformed into a multivariate normal with linear dependencies (i.e. full covariance matrix) by expressing it as an autoregressive model
\(z_d = \mu _d(\mathbf {z}_{< d})+ \sigma _d(\mathbf {z}_{ < d})\ast \epsilon \) 
